I usually take off the glow ignitor right after I start the engine, but today I left it on the engine for awhile before I took it away.
Few minutes later I saw smoke coming out from the glow ignitor. Obviously the battery has shorted because it was very hot too. Also, when I tried to start to engine again the glow plug is dead too. (the plug was close to brand new).

Does anyone have any idea what happened?? Is the ignitor battery killing the plug or the plug shorted the ignitor battery?
That two possibilities might sound ridiculous; I just want to know what went wrong.

Couldn't say; I've never heard of it happening before. How long was the igniter on the running engine? (How hot did it get?)

If the ignitor got too hot (from the engine heat) it could have caused the battery to vent.
Dennis-

Well... the battery in the ignitor will be shot now. (if it got as hot as you indicate... its fried) So you can peel the heat-shrink and pop the battery off the glow ignitor adapter (its pressed on) Then inspect the thing.

It is unlikely that leaving it on your plane was the cause of the ignitor failing. Its probably the spring inside it managed to short to the center wire.

BTW... I have pressed replacemnent batteries onto glw ignotors before. Works fine. That's $2.50 for the replacement cell... vs $12 to $20 to get a new ignitor. (check that insulation thouroughly before trying the replacement cell...)